We study the trace class perturbations of half-line, discrete Laplacian and obtain a new bound for perturbation determinant corresponding non-self-adjoint Jacobi operator. Based on this bound, we Lieb–Thirring inequalities such operators. The spectral enclosure spectrum embedded eigenvalues are also discussed.

For a class of singular potentials, including the Coulomb potential and V (x) = g/x with the coefficient g in a certain range, the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the selfadjoint version chosen. The talk discusses ...

A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as defined on the graph. When the edge lengths have a positive lower bound, all local self-adjoint extensions of the minimal symmetric operator may be classified by boundary condi...

‎Let $\Omega$ be a bounded domain in $R^{n}$ with smooth boundary‎ ‎$\partial\Omega$‎. ‎In this article‎, ‎we will investigate the spectral‎ ‎properties of non-self adjoint elliptic differential operator\\‎ ‎$(Au)(x)=-\sum^{n}_{i,j=1}\left(\omega^{2\alpha}(x)a_{ij}(x)‎ ‎\mu(x)u'_{x_{i}}(x)\right)'_{x_{j}}$‎, ‎acting Hilbert space ‎$H=L^{2}{(\Omega)}$. Dirichlet-type boundary conditions‎. ‎Here‎...

In 2005, Shen introduced a new invariant, G(N), of a di use von Neumann algebra N with a xed faithful trace, and he used this invariant to give a uni ed approach to showing that large classes of II1 factors M are singly generated. This paper focuses on properties of this invariant. We relate G(M) to the number of self-adjoint generators of a II1 factor M : if G(M) < n/2, then M is generated by ...

we give some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(c_{omega_1,varphi_1}^*‎ , ‎c_{omega_2,varphi_2}^*)$ on the hilbert space $mathcal{h}$ of analytic functions is supercyclic‎.